Now,I am a mechanical engineer with very little/no idea of how the processing code goes about in establishing the bluetooth device on my laptop as master. In simple words,it looks like the processing code controls the devices in-built in my laptop whereas the arduino code controls the signals to and from the arduino.Is that right?

The short answer is: information security. If you own the laptop, you might not want to go connecting to any random (potentially hostile, malware-laden) bluetooth device that wanders into range. Likewise if you own a bluetooth device (say, your insulin pump) you might not want anyone with a laptop to gain control of it. Entering the code secures ONE of those connection directions (usually convinces the device that the laptop is an "authorized" thing to talk to) but in an ideal world, both the laptop and the device would generate a code, and you wouldenter each code on the other device for bidirectional security.
-Jeff